1

Part of 2011 Akdeniz University MO

Problems(2)

Source:

a

be a positive number, and we show decimal part of the

\left\{\frac{1}{x}\right\}

\left\{a\right\}

.For a positive number

x

\left\{x^2\right\}

\left\{\frac{1}{x}\right\}

\left\{x^2\right\}

.Find value of the

x(x^7-21)

number theorynumber theory unsolved

Source: AUMO 2011

m,n

positive integers and

p

prime number with

p=3k+2

p \mid {(m+n)^2-mn}

p \mid m,n

number theoryprime numbers